A120463 Expansion of x*(1+x+2*x^3) / ((x-1)*(1+x)*(3*x^2-1)).

0, 1, 1, 4, 6, 13, 21, 40, 66, 121, 201, 364, 606, 1093, 1821, 3280, 5466, 9841, 16401, 29524, 49206, 88573, 147621, 265720, 442866, 797161, 1328601, 2391484, 3985806, 7174453, 11957421, 21523360, 35872266, 64570081, 107616801, 193710244

Offset: 0

Author

Roger L. Bagula and Gary W. Adamson, Jun 30 2006

Keywords

• nonn
• easy

Comments

Top element of the vector obtained by multiplying the n-th power of the 5 X 5 matrix [[0, 1, 0, 0, 0], [1, 0, 1, 0, 0], [0, 1, 0, 1, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0]] by the column vector [0, 1, 1, 2, 3].

Links

• Index entries for linear recurrences with constant coefficients, signature (0,4,0,-3).

Crossrefs

Cf. A003462, A134931.

Programs

Mathematica

LinearRecurrence[{0,4,0,-3},{0,1,1,4,6},40] (* Harvey P. Dale, Dec 15 2018 *)

Formula

G.f.: x*(1+x+2*x^3) / ((x-1)*(1+x)*(3*x^2-1)).

a(2n+2) = A134931(n). a(2n+1) = A003462(n+1). - R. J. Mathar, Nov 07 2011